We recently purchased a Italian Greyhound Puppy and been trying to housebreak him, but he will absolutely not poop on the grass, he will only go on my deck, cement, or something else that is hard. How can I train him to go in the grass? He'll pee in the grass happily.

Don't know but he may change as he gets older, just console yourself with the fact that it is easier to clean the concrete

It sounds as if he's been raised in an area with little or no grass - this is often a problem with puppies, as they tend to stick with what they know.  For the first time this year I sectioned off my grass area for the winter, and my 12 year old dog didn't 'go' for 36 hours until she'd worked out how to get through the fence to the grass..........

You could try moving some poo onto the grass, and/or rubbing some wee onto it.

We have a similar problem with our Cairn terrier (nearly 5 months old)  he will only relieve himself (poo and pee) on gravel, scrub land or in the flower beds. Actually I don't mind too much as the urine would ruin the lawn (try saying that after a couple of drinks) and as Jackie says concrete is easier to clean up and wash down.

Congrats on your choice of dog I think Italian Greyhounds are absolutely adorable!
Why not take him out to the grass on his lead and wait and wait, sooner or later he'll have empty himself, either that or explode lol. Wait for a time when you know he'll busting to go like first thing in the morning,  after a meal, or after a nap. When he does eventually do it, go over the top with praise and give a treat so he knows he's done good. Also, as someone else suggested, scoop up poo from the deck and put it on the grass to scent it. Good luck.